The figure suggests the solution. Reflect D on sides {AC,AB} to obtain points {D

To prove this, take the reflexions {HB,HC} of line BC with respect to sides {AB,AC}. They intersect at a point H and line AH is easily proved to be orthogonal to side E

The results on the envelope can be generalized for a segment of fixed length gliding on side BC. This is discussed in ReflectingSegmentEnds.html .

Similarly_Rotating.html

ParabolaChords.html

Parabola.html

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